铁磁性的磁滞：某些双尺度Landau-Lifshitz模型的渐近性
Hysteresis for ferromagnetism: asymptotics of some 2-scale Landau-Lifshitz model
摘要：
我们研究了一个2尺度版本的Landau-Lifshitz系统的铁磁性，引入Starynkevitch建模磁滞：磁化强度的响应是快速相比，缓慢变化的应用磁场。考虑交换项，在空间维3中，我们证明了在系统平衡点的自然稳定性假设下，系统的强解遵循这些平衡点的动力学.我们也给出了明确的例子，相关的平衡和外部磁场，当铁磁介质占据一些椭球域。
英文摘要：
We study a 2-scale version of the Landau-Lifshitz system of ferromagnetism, introduced by Starynkevitch to modelize hysteresis: the response of the magnetization is fast compared to a slowly varying applied magnetic fi eld. Taking the exchange term into account, in space dimension 3, we prove that, under some natural stability assumption on the equilibria of the system, the strong solutions follow the dynamics of these equilibria. We also give explicit examples of relevant equilibria and exterior magnetic fields, when the ferromagnetic medium occupies some ellipsoidal domain.
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